### How to plot derivative and antiderivative of a spline

Suppose I have a spline like that:

```
from sage.gsl.all import spline
values = [(-3,-2),(-2,0),(1,2),(3,1),(4,5)]
interpolation = spline(values)
plot(interpolation,(-3,5)) + list_plot(values)
```

What's the easiest way to plot the derivative and the antiderivative functions of the spline?

Note that I want just the plot, not a symbolic expression of both, so numerical methods should apply. However getting a symbolic expression would be the best.

How can I find maxima, minima and roots of the spline? Numerically would be good enough.